3 added 417 characters in body
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a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[ Arrow /@ Table[{{2 Cos[θ], Sin[θ], 0}, 2 {2 Cos[θ], Sin[θ], 0}}, 
                               {θ, 0, 2 π, π/10}]]

Show[a, b]

enter image description here

It is unclear whether you'd prefer this:

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]];

b = Graphics3D[
   Table[Arrow[{{3.05 Cos[\[Theta]], Sin[\[Theta]], 
       0}, {3.05 Cos[\[Theta] + \[Pi]/10], Sin[\[Theta] + \[Pi]/10], 
       0}}], {\[Theta], 0, 2 \[Pi], \[Pi]/10}]];

Show[a, b]

enter image description here

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[ Arrow /@ Table[{{2 Cos[θ], Sin[θ], 0}, 2 {2 Cos[θ], Sin[θ], 0}}, 
                               {θ, 0, 2 π, π/10}]]

Show[a, b]

enter image description here

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[ Arrow /@ Table[{{2 Cos[θ], Sin[θ], 0}, 2 {2 Cos[θ], Sin[θ], 0}}, 
                               {θ, 0, 2 π, π/10}]]

Show[a, b]

enter image description here

It is unclear whether you'd prefer this:

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]];

b = Graphics3D[
   Table[Arrow[{{3.05 Cos[\[Theta]], Sin[\[Theta]], 
       0}, {3.05 Cos[\[Theta] + \[Pi]/10], Sin[\[Theta] + \[Pi]/10], 
       0}}], {\[Theta], 0, 2 \[Pi], \[Pi]/10}]];

Show[a, b]

enter image description here

2 deleted 35 characters in body
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a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[
  Arrow /@ Table[{{2 Cos[\[Theta]]Cos[θ], Sin[\[Theta]]Sin[θ], 0}, 
     2 {2 Cos[\[Theta]]Cos[θ], Sin[\[Theta]]Sin[θ], 0}}, {\[Theta], 
 0, 
                              {θ, 0, 2 \[Pi]π, \[Pi]π/10}]]

Show[a, b]

enter image description here

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[
  Arrow /@ Table[{{2 Cos[\[Theta]], Sin[\[Theta]], 0}, 
     2 {2 Cos[\[Theta]], Sin[\[Theta]], 0}}, {\[Theta], 0, 
      2 \[Pi], \[Pi]/10}]]

Show[a, b]

enter image description here

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[ Arrow /@ Table[{{2 Cos[θ], Sin[θ], 0}, 2 {2 Cos[θ], Sin[θ], 0}},  
                               {θ, 0, 2 π, π/10}]]

Show[a, b]

enter image description here

1
source | link

a = Graphics3D[Ellipsoid[{0, 0, 0}, {3, 1, 2}]]

b = Graphics3D[
  Arrow /@ Table[{{2 Cos[\[Theta]], Sin[\[Theta]], 0}, 
     2 {2 Cos[\[Theta]], Sin[\[Theta]], 0}}, {\[Theta], 0, 
     2 \[Pi], \[Pi]/10}]]

Show[a, b]

enter image description here